Present Value

Those, approximately, were the first words to come out of my mouth after hearing about the Cubs signing the soon-to-be 31-year-old slugger. After a few offseasons of fiscal sanity, owners flush with cash have decided to bust their wallets open and throw money left and right. Soriano’s contract is the biggest signed since the infamous 2000-01 offseason, when five players—Alex Rodriguez, Derek Jeter, Manny Ramirez, Todd Helton, and Mike Hampton—all received nine-figure deals worth a combined $863.5 million.

So damn. That was my initial reaction. Then I asked myself, well how much did he really get? Soriano’s contract calls for him to receive $17 million a year, but as you might imagine, $17 million in 2014 is not the same as $17 million in 2007. That’s why lottery winners often take a lump payment of about half their winnings instead of the total value of their ticket paid out over a number of years. Inflation renders the same amount of money in the future less valuable than it is today. A hundred dollars could buy you a whole lot more in 1906 than it can in 2006 (actually, $100 in 1906 is equivalent to about $2,050 these days).

What’s more is that while the modern rate of inflation in the United States is pretty low—about 3% a year—baseball inflation is pretty rampant at about 10%. That is, a player who would get a $10 million contract last offseason should be expected to receive $11 million this offseason. Well then, imagine what he should be expected to get in say, 2014! (Over $21 million, actually.)

So to evaluate any contract, the first thing we have to do is to convert it into 2007 dollars. Economists do this all the time, and they call it present value, which is the value of a given amount of future money today.

Assuming Soriano gets $17 million each year (and reports say that the contract is heavily back-loaded, which would only drag down the present value of the contract further), the present value of his deal is a little under $100 million over eight years. $12.5 million a year does sound more palatable than $17.

Many complaints about Soriano’s contract have focused on the fact that he received more dollars than Carlos Beltran did two years ago, despite not being nearly as good a player. Well, in fact, this is wrong. If we translate Beltran’s deal into 2007 dollars, Beltran got $110 million, $10 million more than Soriano, for one less year. In present day value, Beltran is being paid $3 million more per year.

But that presents us with two questions: Is Beltran worth $3 million more per year than Soriano, and is Soriano worth $12.5 million a year? Well, according to my calculations, Soriano has an established performance level of about 3.0 wins above replacement; Beltran had an established performance level of about 3.4 when he was signed. In that case, Soriano is being paid a little over $4 million per marginal win, while Beltran got paid $7.5 million per marginal win over Soriano. On the other hand, Beltran has blown away his previous established performance level, and is now at about 4.4 wins above replacement, which translates to just over two million dollars per marginal win over Soriano.

Well, that’s a bunch of numbers but no real answers. OK, here’s my take: the difference between the dollars received by Soriano and Beltran is about right, but both are overpaid. However, both were signed for about the going rate for a free agent, which is higher than the actual value (in terms of increased revenue) of a marginal win.

Well, since I did all the work, we might as well have some fun with these numbers. For example, how much is Alex Rodriguez’s fabled 10-year, $252 million contract worth in 2007 dollars? $300 million. What’s more is that if he were to sign a 10-year contract this offseason, to receive a present value of $300 million A-Rod would have to get a $446 million deal. Makes Soriano’s contract sound like peanuts, huh?

Rodriguez, by the way, had an established performance level of 6.4 wins above replacement when he was signed, and has been worth 6.9 wins above replacement per year since. So he was paid about $4.7 million (in 2007 money) per marginal win, versus $4.6 million for Beltran and $4.2 million for Soriano.

Manny Ramirez’s eight-year, $160 million contract prior to the 2001 season has a present value of $208 million, and he would have to get a $283 million contract this offseason to match that. Ramirez’s established performance level was 5.0 wins above replacement a year, and he’s matched that exactly in the first six seasons of his deal, so Manny got paid $5.2 million per marginal win.

And how about Kevin Brown’s seven-year, $105 million contract, the first nine-figure deal in major league baseball history? Well, Brown’s contract was worth $172 million in 2007 dollars, and he would have had to receive a $225 million contract this offseason to match that. Yuck.

If you want to talk about a good deal, Helton’s contract has a present value of $16.2 million a year, and so far he’s been worth 7.0 wins above replacement per season, for a cost of just $2.3 million per marginal win. Helton’s established performance level for 2007 is more like 5.3 wins above replacement, which would still mean a cost of just $3 million per marginal win, better than any of the above deals for sure.

Just for fun, let’s end this article with a look at just one more thing: Player salaries over time. For example, how much was Ted Williams’s famed 1955 contract for $98,000 worth in 2007 dollars? Try $14 million, more than Soriano (as it should be, of course). Baseball Reference has salary data going back to 1985, and I’ve calculated the present value of the highest-paid player in baseball for each of those years. Enjoy.